I’m going to explain the Reverse Landfill Matrix Mixer, since that’s the one I have, but once you understand it, you’ll likely be able to mostly understand other matrix mixers. Here’s an annotated photo of the one I built:
Notice the colors I used for knobs and for the output jack nuts. Those are the color conventions I decided to use for mine, to help me keep track of things better, but I could have made it go RBG or BGR or whatever order I wanted, or I could I left it not-color-labeled, since no channel needs to be a color channel (that’s just a convenient way to use a matrix mixer in the video world).
In my annotated pic, I’ve circled the rows in green to show that each input goes to a whole row of knobs. And I’ve circled each column in pink to show that each column goes to a separate output. This is how colorization can work, if you connect each of the three outputs to a different color channel. Then you have three separate channels of colorization. (The Reverse Landfill Matrix Mixer also has a fourth input channel which is inverted. A luma signal into this channel will remove its signal from the output mixes. It’s a little trickier to comprehend in terms of colorization, and I don’t use it much myself.)
To colorize a luma output from a Vidiot: Connect each output of the matrix mixer to a separate color channel. Connect your luma signal to the first input of the matrix mixer. Now each of the three knobs in that first row adjust how much of that input signal is sent to each output, and since each output is a separate color channel, you can dial in the amount of R, G, and B.
To mix two luma signals: Connect your first luma signal to the first input of the matrix mixer. Connect your second luma signal to the second input of the matrix mixer. If you just want a single luma output, take your output from the first output of the matrix mixer. Now if you adjust the first knob in the first and second rows, you control how much of those two luma signals come through into the output luma signal. If you want to colorize and mix the two luma signals, connect each output of the matrix mixer to a separate color channel. Then the all three knobs in first row colorize the first luma input, all three knobs in the second row colorize the second luma input, and the output is those two colorized signals mixed together.
As far as videos, I urge you to check out the 3 Patches video for the LZX Color Chords, since that is a matrix mixer as well. Color Chords (CC) differs from the Reverse Landfill Matrix Mixer (RLMM) in a few ways: CC doesn’t have the inverted input channel that the RLMM has as input 4. Unlike the RLMM, the CC has a layer 4 input that isn’t inverted, doesn’t have any controls, and can be input to each color channel separately. (This means you can chain multiple CC’s together for more inputs/layers, or you can chain other RGB signals in as the background layer.) CC has a neat opacity feature that RLMM doesn’t have. (For the CC to work like the RLMM, all the opacity sliders need to be all the way down, I think.) CC’s layout and panel are more focused on colorizing, whereas RLMM’s is more generic by design since it was designed to be used as a feedback mixer (an area I have yet to explore) or a colorizer. (As I understand it, the inverted input channel is very useful for feedback mixing.)
The Reverse Landfill Cmix is a more traditional mixer with one knob per input and a single output, though designed for video signals. (The Cmix technically has two outputs, but the second output is a copy of the first, unlike in the RLMM where each output is separate.) If you just want traditional mixing instead of matrix mixing, the Cmix takes up less space than the RLMM and has 3 inverted inputs as opposed to RLMM’s 1 inverted input.
I think I touched on all (or at least most) of your questions. Do feel free to ask follow-ups if you have any. Hopefully this helps some!